We have previously described techniques for displaying an image holographically (see, for example, WO 2005/059660, WO 2006/134398, WO 2006/134404, WO 2007/031797, WO 2007/085874, and WO 2007/110668, all hereby incorporated by reference in their entirety). They have a range of applications including, for example, in hand held battery powered devices such as digital cameras, mobile phones, portable media players, laptop computers and the like.
Broadly speaking in this technique an image is displayed by displaying a plurality of holograms each of which spatially overlaps in the replay field and each of which, when viewed individually, would appear relatively noisy because noise is added (by phase modulation) prior to a holographic transform of the image data. However when viewed in rapid succession the replay field images average together in the eye of a viewer to give the impression of a reduced (low) noise image. The noise in successive temporal subframes may either be pseudo-random (substantially independent) or the noise in a subframe may be dependent on the noise in one or more earlier subframes with the aim of at least partially cancelling this out, or a combination of both may be employed. More details of such OSPR (One Step Phase Retrieval)-type procedures and the associated ADOSPR (adaptive OSPR) are described later.
The conventional ADOSPR approach functions by sequentially considering whole colour planes of the input image, which (subsequent to appropriate pre-processing) are embedded in a frame of suitable size (e.g. 1024×1024 pixels), from which a number of hologram subframes are produced. Each hologram subframe is the same resolution as the frame, and its computation necessitates a Fourier transform of that size. Due to the nature of the implementation of the fast Fourier transform operation in hardware, a large, fast memory is required to store the fully-complex intermediate data produced. The memory bandwidth required makes an off-chip implementation difficult, while the memory size required would make an on-chip implementation uneconomical.
Additionally, while holograms produced in this manner may exhibit good performance in simulation, in reality the images produced will exhibit the phenomenon of inter-pixel interference, compromising the uniformity and readability of images. Such a phenomenon results from optical system aberrations resulting from non-flatnesses in the SLM surface and lenses: such aberrations cause the system's point spread function (PSF) to increase in spatial extent, with the result that spots from adjacent pixels now overlap. Because the spots are coherent, they interfere with each other, and because the associated target pixels have random phase, the interference consists of random regions of constructive and destructive interference which appear as blotchiness in the output. (This effect is referred to by some authors as “speckle”. However, the effect has nothing whatsoever to do with the phenomenon of laser speckle, in the usual sense of the term, which results from interference of coherent light on the eye's retina, subsequent to scattering from a rough surface.) The approach described in the applicant's pending application GB 0706264.9 published as GB 2448132 (incorporated herein by reference) corrects for inter-pixel interference by taking the system's PSF into account, but if the PSF is not known exactly, as is the case when non-systematic non-flatnesses are present in the system, its efficacy is significantly reduced.
A two-dimensional encoding method for hologram recording is described in JP09197947.